Off On A Tangent

At a recent Year xi Parents' Evening, I was guilty of hypocrisy. I reassured parents that their daughters would move rattling good prepared for their maths GCSE because we'd move doing one-half a term of revision lessons. Most parents nodded happily, but 1 dad challenged me. He asked why I didn't convey the chance to learn his fille some calculus. Good point! I've written many times most the importance of imparting mathematical noesis without focussing on exams (a 'no teaching to the test' philosophy), in addition to in that location I was promising an extended menstruation of revision instead of mathematical enrichment.

I don't desire to learn my students to exceed exams. I desire to learn them mathematics, in addition to I desire passing exams to move a welcome by-product of that. But what if some of my students neglect to run into their potential inwards their GCSE exams this summertime every bit a number of my determination to trim revision time? It's a dilemma.

Bitesize enrichment
The twenty-four hr menstruation later Parents' Evening I'd planned a criterion lesson on algebraic proof amongst my Year 11s (by 'standard' I hateful explanation, examples in addition to practice). At the starting fourth dimension of the lesson, past times agency of introducing the topic of proof, I mentioned that many mathematicians pass their lives working on proofs. As I said it I was reminded of the BBC Horizon episode blog post most teaching a lesson on Fermat.

It was alone 10 minutes of spontaneity inwards a lesson, but thus rattling worth it. My students went abode from schoolhouse having learnt something novel most the world, in addition to that's what instruction is all about.

The success of this unplanned tangent gave me the confidence to starting fourth dimension diverting from my lesson plans all over the place. In a Year 10 lesson on percentages I got carried away explaining how banks brand coin from involvement charge per unit of measurement spread. I know a lot most finance from my previous career thus I felt confident talking most this. But I acknowledge that my noesis of 'non-curricular' mathematics is limited. I possess got a pile of mathematical books that I'm desperate to read but never acquire time. Reading around your bailiwick gives yous the noesis in addition to confidence to become off on these interesting tangents. I must read more! If you're on Twitter in addition to thus do acquire involved in @MathsBookClub for encouragement in addition to inspiration.

How good read are you? Book recommendations from matheminutes.blogspot.co.uk.

Barriers to spontaneity

I don't deny that schemes of operate are necessary. For 1 thing, they ensure essential coverage of all the topics required for populace exams. In addition, synchronisation of teaching allows simultaneous assessment of whole twelvemonth groups, in addition to gives orbit for departmental collaboration. Schemes of operate are too a machinery for implementing a maths department's teaching strategy or philosophy. So they are 'a good thing' even though they may underpin a frustrating lack of freedom.

I was of late teaching 3D trigonometry to a top laid Year ix (very smart girls - many volition convey their GCSE inwards Year 10). I was going through the event below from CIMT. When nosotros got to purpose (d) nosotros drew out the triangle inwards inquiry in addition to established that it was non-right angled. They haven't done the Sine in addition to Cosine Rules soundless thus I said we'd skip it. I told them that they'd comprehend non-right angled triangles side past times side twelvemonth in addition to they accepted that without question. 

It's a chip wretched isn't it? I was disappointed past times their lack of intellectual curiosity, but to a greater extent than disappointed amongst myself for telling them they'd possess got to expect a twelvemonth to complete solving the problem. Why didn't I simply launch into teaching the Sine in addition to Cosine Rules? Firstly, because of fourth dimension pressure level - the aeroplane would possess got fallen behind their peers if we'd spent an extra calendar week or 2 on trigonometry, putting them at a disadvantage inwards their side past times side Year ix assessment (this would possess got upset them). Secondly, inconsistency of topic coverage would do problems for side past times side year's teachers. Thirdly, I hadn't idea inwards advance most how I'd learn non-right angled trigonometry. It takes a rattling confident in addition to experienced instructor to deliver a proficient lesson off the cuff. I demand at to the lowest degree 10 minutes thinking fourth dimension earlier I teach! So I left it at 'we'll do it side past times side year'. Most unsatisfactory.

To some extent, schemes of operate bound our might to become off on interesting mathematical tangents. But it could move worse. We could move forced to utilisation pre-written lesson plans, slides in addition to resources. I bask designing tailor-made lessons for my students. I similar having orbit to move creative in addition to I similar beingness able to divert from my programme during a lesson if I desire to. It's overnice to possess got this autonomy. Ideally our schemes of operate are flexible plenty to adapt these worthwhile diversions. If you're designing a system of operate for side past times side year, acquit this inwards mind. Time for tangents is most welcome.

Enrichment

momath.org

I acknowledge to knowing real piddling close how schoolhouse finances work. Some schools own got hundreds of iPads, others own got leaking roofs. It's all a mystery to me. Due to budgetary constraints I've solely been on ane maths schoolhouse trip inward the concluding 5 years. This leads me to wonder how of import enrichment is, in addition to what schools tin give the axe create when coin is tight.

Why enrichment?
When I was a teenager I did nada inward maths beyond what was needed to go past times my exams. Apart from a dyad of maths competitions, my schoolhouse did non 'enrich' our mathematics education. I liked maths because I was proficient at it - maths lessons were my comfort zone. I enjoyed the satisfaction of solving problems but I had no involvement inward mathematics exterior the classroom. I await that many of my electrical flow students experience the same way.

Maths In Action

H5N1 dyad of years agone I accompanied a grouping of xx Year 12 students to a twenty-four sixty minutes catamenia of Maths inward Action lectures. I saw amazing speakers including Simon Singh in addition to Hannah Fry. I'm convinced that this trip made me a meliorate maths teacher. Not solely did I larn loads of cool novel stuff to portion amongst my students, I also gained a novel enthusiasm for mathematics. I'm certain at to the lowest degree some of my Year 12 students must own got felt inspired too. Perhaps they went on to report maths at academy every bit a result.

Education is all close making students to a greater extent than knowledgeable, so nosotros should portion mathematics inward all its glory - non only the content of the examination syllabus. I've written close these ideas earlier inward my post service Off on a Tangent. We must give our students opportunities to appreciate the wonders of mathematics.

There are loads of brilliant places for mathematical schoolhouse trips. Bletchley Park is a wonderful example. The Mathematics Gallery at the Science Museum is due to go out the world's initiative of all mathematics gallery afterwards a recent £5 ane M 1000 donation, so volition no uncertainty go out an outstanding finish for schoolhouse trips. The MathsWorldUK projection is also exciting. Maths Inspiration events are brilliant. Sometimes though it's non practical or affordable to own got students out on trips. Bringing speakers into schoolhouse is a proficient alternative.

A persuasion of the novel Mathematics Gallery

In-School Speakers
H5N1 piece agone I asked Twitter close maths speakers in addition to I was real grateful to have dozens of useful replies. I've listed a pick of speakers below. Costs are typically inward the part £200 - £600.

Kjartan Poskitt

Kjartan Poskitt, author of Murderous Maths, comes highly recommended. Talks include 'Isaac Newton in addition to his Falling Apple' in addition to 'Mayhem amongst Maths in addition to Music'. In his Murderous Maths sessions he performs a diverseness of features from his Murderous Maths books including flexagons, magic squares, foreign disclose facts, knots, tricks, amazing disclose predictions in addition to so on. Full details are available on his website.

Matt Parker (@standupmaths) runs Think Maths, a group of fantastic speakers who view schools to perform maths talks in addition to workshops for all ages in addition to abilities. Topics hit from topology, disclose theory in addition to probability to magic in addition to maths inward pop culture.

James Grime (@jamesgrime) travels extensively giving world talks all over the world. Details of fees in addition to workshops are available on his website. For trial 'The Enigma Project' is a presentation close the history in addition to mathematics of codes in addition to code breaking including a demonstration of an master copy WWII Enigma Machine, followed past times code breaking workshops. It's suitable for pupils of all ages in addition to abilities from Key Stage ii to Key Stage 5.

Bletchley Park (@BletchleyParkGB) offers 'Enigma Outreach' inward which they convey a genuine, working Enigma machine to your school. Visits are built only about the demonstration of this iconic slice of World War II history, in addition to tin give the axe also include presentations on the history of Bletchley Park, interactive talks on codes in addition to ciphers, in addition to hands on codebreaking workshops. Full details in addition to fees are available here.

Colin Beveridge (@icecolbeveridge) offers 'Games, Goats in addition to Gold' which uses pop game shows to demonstrate that thinking clearly close probability isn’t only proficient for your exams, but has applications inward the slightly-more-real but only every bit arbitrary globe of prime number fourth dimension TV. The workshop is aimed at brilliant Year nine students, but tin give the axe last adapted for most secondary schoolhouse groups. Details of this verbalize in addition to others are available on Flying Colours Maths.

Colin Wright (@ColinTheMathmo) comes highly recommended. He offers a collection of talks in addition to workshops that hit from ages xiii in addition to onwards. One of his most pop talks, 'Juggling: Theory in addition to Practice' is close the mathematics of juggling. Further data close his hit of talks is available on his website.

Colin Wright

Dr Matt Pritchard (@ScienceMagician) is an award-winning magician, comedian in addition to creative communicator. He delivers talks inward schools on both maths in addition to scientific discipline topics. His maths talks include 'Magical Maths' in addition to 'The Man Who Cannot Lose'. He also has a session aimed at D1 students - 'From Facebook Friends to Postman Pat'. Full details are available on his website.

Rob Eastaway (@robeastaway) is the writer of a disclose of mathematical books and the Director of Maths Inspiration, a national programme of interactive lecture shows. He offers a fantastic pick of in-school talks including 'What's the indicate of maths?', 'When Maths Meets Psychology', 'Maths on the Back of an Envelope' in addition to 'From Pepsi to Peace Deals'. Many of his talks are suitable for Sixth Form students. See his website for to a greater extent than information.

Ben Sparks (@SparksMaths) plant part-time amongst the Further Maths Support Programme as a speaker, tutor in addition to co-ordinator, in addition to part-time every bit a freelance maths enrichment speaker only about the United Kingdom of Great Britain in addition to Northern Ireland of Britain in addition to Northern Republic of Ireland – including with Maths Inspiration. His talks, including 'The Creation of Number' in addition to 'Pretty Irrational' are listed on his website. 

Puzzle Days in addition to Workshops
If yous own got a proficient laid upwardly of resources so yous may last able to run puzzle workshops yourself (FunMaths Roadshow materials are solely £27). Alternatively, at that spot are companies who tin give the axe come upwardly to your schoolhouse to run workshops for yous - hither are some examples:

The 7puzzle Company (@7puzzle) delivers fun in addition to effective maths workshops inward both principal in addition to secondary schools all over the UK. The games played non solely challenge children’s disclose skills, but also deed every bit a confidence-builder. They comprise strategy, logic, shape in addition to space, retention in addition to visual aspects every bit good every bit helping children to focus on the social etiquette of communicating, listening, turn-taking, sharing in addition to team-working piece participating inward the activities. Further data close the 7puzzle experience is available here.

The 7puzzle experience

MMP Hands-On Maths Roadshow (@mathsroadshow). The NRICH Hands-On Maths Roadshow is a collection of hands-on mathematical puzzles, games in addition to activities that tin give the axe last brought to schools for a exceptional maths event. Roadshow activities are designed to promote creative approaches to mathematics in addition to strategic thinking in addition to to own mathematical curiosity. The Roadshow tin give the axe last tailored to suit diverse historic catamenia ranges, from Key Stage 1 to 4. The fee is £595 for a amount twenty-four sixty minutes catamenia in addition to £415 for a one-half twenty-four sixty minutes catamenia - amount details are available here.

The Problem Solving Company (@problemsolveit) offers fun filled days of hands-on maths challenges to students from Early Years to KS3. Their maths puzzle days promote thinking, logical reasoning in addition to mathematical agreement amongst an emphasis on teamwork in addition to discussion. They also run Year 6/7 Transition Days in addition to Sixth Form Team Building Days. Further data in addition to prices are available here.

The Problem Solving Company

Happy Puzzle Company (@happypuzzle) also runs Puzzle Challenge Days for Schools - click here for details.

Maths competitions - local in addition to national - are some other neat source of enrichment, though they oft involve solely a handful of high-attainers. It's worth offering opportunities to whole yr groups too.

Affordable enrichment
Don't forget that your nearest Maths Hub mightiness run enrichment events. For trial the Surrey Plus Maths Hub runs Inspiration Days (featuring speakers such every bit Matt Parker) that students tin give the axe attend for complimentary - spaces are available on a kickoff come, kickoff served basis.

Look out for grant schemes also - your schoolhouse could have fiscal assistance to run maths enrichment events.

This post service past times no agency represents an exhaustive listing of speakers in addition to workshops. If you're looking for enrichment opportunities so you'll notice a plethora of providers inward the STEM Directories. If yous own got whatsoever recommendations from personal experience so delight comment below.

5 Maths Gems #33

Hello as well as welcome to my 33^rd gems post. This is where I portion 5 education ideas I've seen on Twitter.

Well it's been fun education inwards this week's heatwave hasn't it?! I long for an air-conditioned classroom. Still, all this lovely sunshine serves every bit a prissy reminder that the summertime holidays are simply some the corner.

1. Pythagoras Pile Up
We've all seen the fantastic #mathsconf4 I was fortunate to listen a fantastic persuasion for education Fractions, Decimals as well as Percentages from Number Resources page.

This calendar week @solvemymaths shared a actually prissy persuasion for education estimator skills which comes from @Ms_Kmp's website mathssandpit.co.uk. Have a expect at her post 'Calculators: The New Hope' to download the resource. And cheers to @solvemymaths for his novel '7 Days of Maths' series, which is good worth following.

4. Maths Videos
Thanks to @mhorley for sharing a link to the BBC's Kick Sum Maths videos - I've non seen these before. They powerfulness come upwardly inwards handy to back upwardly the education of a break of Key Stage 2/3 topics.

5. Self-Descriptive Numbers
Thanks to @LearningMaths for sharing this lovely activity 'Self-descriptive numbers'.

If yous expect through the set of resources from which this activity comes as well as thus you'll encounter that there's enough of other bully materials inwards at that topographic point too.

If yous similar these resources as well as thus you'll beloved cleavebooks.co.uk/trol which is total of splendid activities. For illustration I've long been a fan of the Vocabulary Exercises which would function good inwards an information technology Room or amongst iPads.

Recommended Reading
Here's some links to banking concern jibe out:

• Bruno Reddy (MEI Conference, Pret homework, #mathsconf4 and Favourite Problems. My final gems post - Gems 32 - was 1 of my most pop posts ever.

Finally, I desire to portion a Don Steward activity that I institute peculiarly effective this week. I was running an Influenza A virus subtype H5N1 score induction session as well as decided to role the query below every bit a starter to brand a indicate well-nigh algebra skills. The algebra hither should live on straightforward for students who well-nigh to embark on Influenza A virus subtype H5N1 level, but some students struggled to position the answer. I made the indicate that if yous desire to produce Influenza A virus subtype H5N1 score Maths as well as thus this form of algebra should come upwardly really naturally. Strong algebra skills - ie the powerfulness to produce this activity effortlessly - should live on embedded yesteryear GCSE as well as are essential to every Influenza A virus subtype H5N1 score mathematician.

5 Maths Gems #42

Hello together with welcome to my 42^nd gems post. This is where I portion or together with therefore of the best pedagogy ideas I've seen on Twitter.

1. Resources
To start, a few novel resources that y'all powerfulness non cause got seen.

Miss Norledge (@MissNorledge) drew inspiration from a Maths Feast problem to brand iii coordinate geometry problems of her own. These lovely 'Triangle Regions' tasks are suitable for GCSE students or Year 12s.

The clever folks at MathsPad exceed on to arrive at fantabulous resources - this Always/Sometimes/Never True activity for Fractional Indices is excellent. The solutions furnish really helpful explanations too. I've added this to my resource library.

Here's or together with therefore other slap-up novel resources from MathsPad - How many ways tin nosotros write 1 million? These are fantabulous activities for consolidating cognition of indices together with measure form.

Check out mathspad.co.uk for to a greater extent than fantastic resources. And if you're on Twitter, Nicola (@MathsPadNicola) together with James (@MathsPadJames) are good worth following.

2. Enrichment for Sixth Form Mathematicians
Thanks to Graham Colman (@colmanweb) for sharing his listing of Maths Beyond the Curriculum activities. This listing is written for Year 12/13 - it would hold out specially useful for a educatee who intends to study maths at university. It could easily hold out adapted for other twelvemonth groups too. Here's an extract:

3. m4ths.com
Steve from m4ths.com teaches at Thomas Clarkson Academy inwards Wisbech. He has been sharing or together with therefore bright novel resources recently. Here's a few examples.

His 'A flat page too.

4. Target Stickers
Target grades are an obsession inwards many schools. I'm non a fan. I tell my students to aim for top grades regardless of what their target says. After all, targets are largely based on sweeping generalisations together with dodgy data.

Most teachers (myself included) are regularly required to study on progress against targets. I similar the sticker sentiment below from Charmayne Bailey (@MissBaileyMaths). The scale makes it actually clear to students where they stand, what their minimum target flat is, together with where they're heading.

5. GCSE Revision Ideas
I dear this sentiment from Mel (Some Things I've Tried inwards which I shared or together with therefore novel pedagogy ideas I've been trying this term

In Case You Missed It... in which I shared or together with therefore ideas together with resources that cause got been good received on Twitter

Five to Follow #ff in which I recommended 5 creative maths teachers to follow on Twitter.

I enjoyed participating inwards the minute Maths Journal Club chat - y'all tin read a write-up of the give-and-take here.

I used the fractions activity below amongst my Year 7s (I starting fourth dimension featured this activity inwards my post Thoughts on Teaching Fractions). I was quite taken aback past times how revealing this chore was - it uncovered or together with therefore serious misconceptions.

Ticket sales for my exciting Christmaths Party are going well.  There's alone 25 solar daytime tickets left together with therefore mass now! It's going to hold out a fantastic consequence - come across christmaths.weebly.com for details.

5 Maths Gems #45

Hello together with welcome to my 45^th gems post. This is where I portion 5 maths pedagogy ideas.

1. Circumference
Pi Development and Circle: Introducing Circumference. The latter features animations such equally this:

together with a actually dainty laid of circumference questions.

2. Pinpoint Learning
Causing quite a stir on Twitter over the concluding 2 weeks, @tom_quilter's novel website pinpointlearning.co.uk provides students with personalised inquiry booklets based on seek out results. It's perfect for later a mock exam. You precisely upload students' marks together with the website automatically produces private booklets featuring inquiry on the topics that students demand to operate on. The website is complimentary together with is ready for Edexcel papers, thence if you've of late done an Edexcel mock together with then ambit laissez passer it a go. I've seen many tweets from teachers who've already tried it together with speak real highly of it.

3. Five Minute Mock Analysis
When y'all render mock exams to students y'all mightiness similar to role this first-class Five Minute Mock Paper Analysis from @MathedUp. The file is editable thence y'all tin customise it for your school.

4. C4 Integration
I'm pedagogy C4 integration to my Further Maths flat at the moment. We've precisely done Volumes of Revolution together with I enjoyed making role of props to explicate the concept. Thanks to an catch from Chris Smith (@aap03102), I used paper decorations to demonstrate how a company is formed when a bird is rotated some the x axis.

I used these alongside gifs such equally those shown below.

I likewise enjoyed using constant characters for the starting fourth dimension time. This is an catch from Gems 22. Students who forget the 'plus c' inward their answers are asked to decorate a constant character. Hopefully this volition encourage them non to forget in 1 trial to a greater extent than together with volition brand an interesting display for the classroom wall. Here's a dyad of examples of what my students came upwards with:

5. Snowflakes
These Star Wars snowflake designs are bright together with fifty-fifty characteristic characters from the latest films.

Here's a video most how to bend them:



If you're planning to ambit some snowflake activities at schoolhouse inward the concluding calendar week of term together with then it's a groovy chance to beak most fractals - read Gems 16 for to a greater extent than on this.

Snowflakes tin last a fleck tricky to brand thence y'all mightiness similar these real-life graphs.

Right, I accept mock marker to ambit together with Christmas cards to write thence I improve acquire on. I'll acquire out y'all with this dainty inquiry from @OCR_Maths - what fraction is unshaded?

5 Maths Gems #48

Hello as well as welcome to my 48^th gems post. This is where I part pedagogy ideas as well as resources I've seen on Twitter.

1. UKMT inwards the Classroom
H5N1 few people cause got asked how they tin contain UKMT maths challenge questions inwards their teaching. I've seen iii resources that mightiness live on helpful here:

• Thanks to Lisa Chalmers ‏(@MsChalmersMaths) for telling me almost this resource from Dan Walker on TES. He has taken problems from Junior as well as Intermediate Maths Challenges as well as organised them past times topic inwards a PowerPoint, amongst solutions.

• I've written earlier almost the splendid website DrFrostMaths.com. The resources hither are designed for high attainers as well as many of the worksheets depict questions from maths challenges as well as olympiads.
• I mentioned inwards Gems 4 that Mathster has an online UKMT Maths Challenge Quiz. 

2. 'Grade 9' Paper
Thanks to Steve of m4ths.com for pulling together a set of questions that are aimed at the strongest mathematicians sitting the novel GCSE. There's unopen to lovely questions here.

3. Teaching Ideas
I spotted 2 dainty pedagogy ideas on Twitter. The commencement thought is from Clare Hill (@chilledmaths). For pedagogy or revising calculus, she suggests the following:

Students cause got a slice of newspaper amongst facial expression written at the top. The commencement individual integrates the expression, folds over the top as well as passes it to the side past times side student, who differentiates the facial expression that they see. They as well as hence crimp over the top as well as top it to the side past times side pupil who integrates the expression, as well as hence on... At the terminate the newspaper is unfolded and, if all went well, the facial expression at the top should tally the facial expression at the bottom.

The mo thought - shown inwards the tweet below - was shared past times Liz Gibbs (@Liz_Gibbs). This would go at both primary as well as secondary bird for exploring plans, elevations as well as nets.

Which 3D shape did I press into the clay? Which shapes were non pressed into the clay? How create you lot know? pic.twitter.com/Vq0vyY452b

— Liz Gibbs (@Liz__Gibbs) February 3, 2016

4. Fact of the Day
I was emailed past times Ann Rush (@MissARush) with a GCSE revision thought that they've used at their schoolhouse for several years.

Their 'Maths Fact of the Day' tin live on used inwards a set out of ways inwards the run-up to GCSE exams:

• Print the fact of the hateful solar daytime give to each student
• Laminate large versions as well as display inwards classrooms
• Display the fact of the hateful solar daytime inwards a prominent expanse inwards the maths corridor
• Refer to the fact as well as previous facts inwards lesson starters/plenaries
• Ask cast tutors to part at cast time.

My schoolhouse does a 'Word of the Week' that is displayed all over the schoolhouse - this mightiness go for 'Maths Fact of the Day' too.

5. Feedback Sheets

Grant's (@AccessMaths) novel thought has been actually popular. If you're non on Twitter as well as hence you lot mightiness cause got missed this. He has designed excellent 9 - 1 Feedback Sheets for a large set out of topics. The collection continues to grow. Grant completes a feedback canvas for each pupil later they've done an assessment. They as well as hence answer to his feedback and, amongst access to a assist sheet, consummate the questions provided. Read Grant's recent blog posts for all the details.

Update

If you lot cheque out my late revamped blog archive you'll consider that Jan was a busy blogging calendar month for me. Did you lot select grip of these posts?

• The Joy of Planning
• Handwriting
• New GCSE: Pythagoras Questions
• Classroom Photos - #mathscpdchat
• Five things you lot mightiness non know almost the novel GCSE content #2
• Worries

I also took utilization inwards a podcast amongst Craig Barton which you lot tin nous to here, as well as I announced a Don Steward event at my school, which has forthwith sold out (100 tickets went really quickly).

I'm looking frontward to aid and/or presenting at xi events this year, the commencement of which is #mathsconf6 inwards Peterborough on fifth March. If you lot haven't got a ticket yet, you lot tin learn 1 at mathsconf.com. Watch this infinite for information almost the pre-conference drinks on Fri 4th.

Don Steward late sent me all his PowerPoints on a retentivity stick - best introduce ever! - as well as I've been enjoying looking through them. I'll learn out you lot amongst his lovely activity Circle Remainders: